The use of asymmetric bandwidths \(\mathbf {G} = (G_\ell , G_r)\) 
with \(\mathcal {S}_{\text{M}}(\mathbf {G}) =\lbrace (s, k, e): \,s = k - G_\ell , \, e = k + G_r, \, k = G_\ell , \ldots , n - G_r\rbrace \) 
has been investigated by [1]}.
[2]} propose the following scheme for asymmetric bandwidth selection
based on the Fibonacci series \(\lbrace F_m\rbrace \) 
constructed as \(F_m = F_{m - 1} + F_{m - 2}, \, m \ge 2\)  with \(F_0 = F_1 = 1\) :
The set of asymmetric bandwidths is determined as
\(\mathcal {H}_n = \left\lbrace  (G_\ell , G_r): \, G_{\ell \slash r} = G_{\min } \cdot F_{\ell \slash r}, \, 1 \le \ell , r \le H_n,\quad \text{and} \quad \frac{\max (G_\ell , G_r)}{\min (G_\ell , G_r)} \le C_{\text{asym}} \right\rbrace ,\) 
